Sculptured surface modeling technology is used extensively in the development of a wide variety of consumer and industrial products. However, the methodology for creating surface models has changed very little since these representation schemes were developed nearly thirty years ago (Bohm et al., 1984; Farin, 1988; Faux and Pratt, 1979). Surface models are traditionally generated by various interpolation techniques, based on the coordinate data sampled from a physical model. Consequently, the quality of the surface representation is dependent on the information content of the physical model at the time of data acquisition. Physical models are very expensive, and it is difficult to accurately incorporate changes and refinements of the physical model into the corresponding mathematical representation without completely recreating it. This leads to a rigid design process which inhibits the introduction of simultaneous engineering practices.
As product development cycles are compressed and the associated number of physical models are reduced accordingly, sculptured surface designers are being asked to capture more design information content per prototype. The technology for modification of existing sculptured surface models is well understood (Cohen et al, 1980; Piegl, 1989) as is the link between such models and automated manufacturing process planning (Kim and Biegel, 1988; Wysocki et al., 1989). Furthermore, recent advances in solid geometric modeling is leading to the robust incorporation (i.e., representation) of sculptured surfaces as an integral part of solid geometry (Casale and Bobrow, 1989; Saia et al., 1989).
Unfortunately, relatively few methods exist for the creation of surface models subject to constraints derived from spatial, aesthetic, or other design and manufacturing requirements. Techniques based on classical mechanics (Celinker and Gossard, 1991; Terzopoulos et al., 1987) come closest in spirit to this design paradigm. These techniques allow the designer to control the shape of the surface by imposing boundary conditions and external loads.